S. Stelmastchuk

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20092026

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math.PR2022

Martingales on Principal Fiber Bundles

Pedro Catuogno, Simão N. Stelmastchuk

Let $P (M, G)$ be a principal fiber bundle, let $ω$ be a connection form on $P (M, G)$ , and consider a projectable connection $\nabla^{P}$ on $P (M, G)$ . The aim of this work is to deter…

math.PR2015

Transport Theorem and Continuity Equations: a Stochastic Approach

Pedro Catuogno, Simão N. Stelmastchuk

We give a stochastic generalization of transport theorem on smooth manifold. Furthermore, we deduce a system of continuity equation and present some application on torus.

math.PR2011

Vertical martingales, stochastic calculus and harmonic sections

Simão Stelmastchuk

This work is about a new class of martingales: the vertical martingales. We construct the vertical martingale for smooth submersions and we develop a stochastic calculus for one. F…

math.PR2011

Martingales in Reductive Homogeneous spaces

S. N. Stelmastchuk

The subject of this work is to study martingales in a reductive homogeneous space with respect to a symmetric connection. Our basic idea is to view homogenous spaces as principal f…

math.PR2011

The Itô exponential on Lie Groups

Simão N. Stelmastchuk

Let $G$ be a Lie Group with a left invariant connection $\nabla^{G}$ . Denote by $\g$ the Lie algebra of $G$ , which is equipped with a connection $\nabla^{\g}$. Our main is to intro…